How to mirror a box around given point, not selection center
You can use the CtrlM mirror tool, in Object or Edit mode,  in any orientation, around any pivot-point.


Set the pivot-point .. most likely '3D Cursor', or 'Active Element'
Set the orientation .. if it's not conveniently Local, Global, or other preset, create a Custom Orientation from an edge, or two vertices. (CtrlAltSpace in 2.97, header orientation menu in 2.8)
Locate the pivot-point, by ShiftS snapping the 3D cursor to the right place, or, in Edit mode, making an appropriate vertex from your selection active)
Hit  CtrlM, and  X,Y, or Z. If the orientation is not Global, but the currently selected secondary orientation, hit the dimension twice. (XX, etc.)


You can still go into the tool region to change the orientation, after left-clicking.

In Edit mode, you can achieve the same effect by creating a Custom Orientation from ant two vertices, making your selection, setting the pivot, and hitting SXX-1